N-gonal multilayer symmetric revolute linkage deployed from bundle to surface of revolution

Deployable structures composed of hinge joints (revolute joints) with inclined axis have a potential to realize a rich variety of deformation with a small number of members, which enables it to be lightweight with low-risk of failure. In this paper, a systematic method is proposed to obtain new hinge-jointed structures which have N-dihedral symmetry and can be folded into a straightly bundled shape. The proposed structure, which we call N-MLSRL, is composed of some layers. Each layer is an assemblage of 2N bars and 2N inclined hinges, which can be deformed from a regular 2N-gonal frame into an entirely straight rod shape, which is a generalization of a 4-bar Bennett linkage. For the case N is less than or equal to 3, the N-MLSRL has a single degree of freedom. For an application to design of deployable structures, a method is introduced to generate the structure expanded to a predefined target surface of revolution. For designing the realistic detail considering the finite sizes of the joints, a technique called hinge offsets is used. The proposed method is applied to a horn-shaped structure, a ball-shaped structure and a dome-shaped structure as its numerical examples. The validity of the proposed method is confirmed by a physical model of a dome-shaped structure including hinge offsets.